Dyna mics of neutralizing electrons and focusability of intense ion beams

1. Dynamics of neutralizing electrons and focusability of intense ion beams A.F. Lifschitza, G. Maynarda and J.-L. Vayb aLGPG, Universitė Paris Sud, Orsay, France bLBNL, Berkeley, USA

2. Introduction  Even when the beam is globally neutral, neutralization is not perfect due to the transversal electron temperature → finite screening length  The limit to the neutralization due to finite Te is relevant when: a) global neutralization is good (f ≥90 %) b) transversal temperature is high (Te≥10 keV)  Electron transversal temperature is determined by: a) heating by compression b) flow of electrons into the beam beam electrostatic potential → neutralization degree c) heat exchange with the beam surrounds

3. This work • We study the parallel evolution of the temperature and neutralization: • Isolated beam • Beam interacting with a finite size plasma created by gas ionization • Beam interacting with a electron-source-like plasma Fully-electromagnetic 2-½ PIC simulations (BPIC code) including: a) beam ionization by collision with background gas b) background gas ionization by collision with beam ions and electrons

4. Temperature evolution Isentropic process → Electrons behave as an ideal gas under a adiabatic bidimensional compression →  Isolated beam 2.5 MeV Xe+ , Ib=2.5 kA rb0=5 cm, Lb=50 cm (8 ns) Lf=3 m

5. Close the focal point: 1) Large gradients of density and temperature 2) Electron temperature uncorrelated with density 3) Transfer of energy from radial to axial direction Departures from 2D compression Isolated beam

6. Good values for the neutralization can be obtained assuming: a) infinite beam b) electrons in thermal equilibrium Neutralization Solutions of 1D Poisson-Boltzmann equation: Assuming → Isolated beam

7. Neutralization by gas ionization Plasma and beam compete for picking-up electrons + gas density  + neutralization t<(σ ng vb )-1 Ne / Nb« 1 t>(σ ng vb )-1 Beam interacting with a finite size plasma

8. Temperature evolution Compression overcomes flow-cooling only in the focal region Heat transfer to the plasma tail Beam interacting with a finite size plasma

9. More neutralization & less heating Beam interacting with a e-source-like plasma

10. Summary • Isolated beam: • Isolated beam behaves as a 2D-adiabatic system. • Neutralization values are close to infinite beam in thermal equilibrium. • Departures from 2D compression only visible at the focal region. • Beam interacting with gas ionization plasma: • Neutralization degree proportional to background gas density for early times and independent for later times due to plasma pick-up. • Cooling by electron flow into the beam more significant than compression except in the focal region • Heat transfer to the plasma tail reduces electron temperature inside the beam • Beam interacting with an external plasma: • Gas ionized tail close to an electron source improves beam neutralization and reduces heating by compression

11. Initial evolution of temperature is determined by neutralization evolution Neutralization  Short term neutralization t<(σ ng vb )-1 Ne« Nb  Long term neutralization t>(σ ng vb )-1 neutralization limit for interaction with a electron-source-like plasma approximation for gas ionization plasma Independent of gas density Isolated beam